# On Two Nonintegrable Cases of the Generalized Henon-Heiles System

## Abstract

The generalized Henon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases, new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies searches for the elliptic solutions and allows them to be automatized.

- Authors:

- Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119992 (Russian Federation)
- Central Astronomical Observatory at Pulkovo, St. Petersburg, 196140 (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20692915

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Atomic Nuclei; Journal Volume: 68; Journal Issue: 11; Other Information: Translated from Yadernaya Fizika, ISSN 0044-0027, 68, 2008-2016 (No. 11, 2005); DOI: 10.1134/1.2131124; (c) 2005 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); TN:

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; SINGULARITY

### Citation Formats

```
Vernov, S.Yu., and Timoshkova, E.I..
```*On Two Nonintegrable Cases of the Generalized Henon-Heiles System*. United States: N. p., 2005.
Web. doi:10.1134/1.2131124.

```
Vernov, S.Yu., & Timoshkova, E.I..
```*On Two Nonintegrable Cases of the Generalized Henon-Heiles System*. United States. doi:10.1134/1.2131124.

```
Vernov, S.Yu., and Timoshkova, E.I.. Tue .
"On Two Nonintegrable Cases of the Generalized Henon-Heiles System". United States.
doi:10.1134/1.2131124.
```

```
@article{osti_20692915,
```

title = {On Two Nonintegrable Cases of the Generalized Henon-Heiles System},

author = {Vernov, S.Yu. and Timoshkova, E.I.},

abstractNote = {The generalized Henon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases, new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies searches for the elliptic solutions and allows them to be automatized.},

doi = {10.1134/1.2131124},

journal = {Physics of Atomic Nuclei},

number = 11,

volume = 68,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}

DOI: 10.1134/1.2131124

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